Coordinate note: R1 means row 1, C1 means column 1, and C1R1 is the upper-left cell. The grid is 9×9.
G's clue puts B in the Tool Shed. Inside that area, only one cell is beside a table, so B is fixed there. The Tool Shed now has only one possible cell for G, so G is at R4C1. F must be on a horse in the Training Ring, so F is forced onto the last horse there at R6C6. Then H takes the last mud puddle, R5C3. C's clue tells you a woman is sitting on a horse. That woman must occupy R3C9, so cross out the rest of R3 and C9. At this stage, E and V can both still be that woman. A must be at R9C4. A cannot use R9C8, because C's clue requires C to be one column west of the woman on the horse, putting C in C8. D is then isolated in the final available cell of C5. E must be in the stable, so E takes the horse cell at R3C9. V is then forced into the last remaining cell.